Problem: Solve for $x$ : $x^2 + 18x + 80 = 0$
Solution: The coefficient on the $x$ term is $18$ and the constant term is $80$ , so we need to find two numbers that add up to $18$ and multiply to $80$ The two numbers $8$ and $10$ satisfy both conditions: $ {8} + {10} = {18} $ $ {8} \times {10} = {80} $ $(x + {8}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 8) (x + 10) = 0$ $x + 8 = 0$ or $x + 10 = 0$ Thus, $x = -8$ and $x = -10$ are the solutions.